Certificate for #1245 ⟨a, b | abaab=abba⟩

Completion settings:

• Auxiliary generators:
  1. c = abbaba
• Reduction order:
  • Left-to-right recursive path with deg(a) = deg(c) = 0, a < c; deg(b) = 1

Axiom: abaab=abba.

Defines rule #3.

Referenced by [3], [4], [5], [6], [7].

Axiom: abbaba=c.

Defines rule #6.

Referenced by [3], [4], [5], [6], [7], [8].

Overlap of [1] abaab=abba with [1] abaab=abba:

Critical pair: abaabba=abbaaab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #7.

Referenced by [7].

Overlap of [1] abaab=abba with [2] abbaba=c:

Critical pair: abac=abbababa.

Reduce RHS:

Flip LHS and RHS.

Defines rule #1.

Referenced by [6].

Overlap of [2] abbaba=c with [1] abaab=abba:

Critical pair: abbabba=cab.

Defines rule #9.

Referenced by [8], [9].

Overlap of [2] abbaba=c with [1] abaab=abba:

Critical pair: abbababba=cbaab.

Reduce LHS:

Reduce RHS:

Defines rule #4.

Overlap of [1] abaab=abba with [3] abbaaab=c:

Critical pair: abac=abbabaaab.

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Overlap of [5] abbabba=cab with [2] abbaba=c:

Critical pair: abbc=cabba.

Flip LHS and RHS.

Defines rule #5.

Overlap of [5] abbabba=cab with [5] abbabba=cab:

Critical pair: abbcab=cabbba.

Flip LHS and RHS.

Defines rule #8.